Improve Number Sense and Attention using Visuals: T1I S1 E9

Cheri Dotterer 0:00
Coming up on today's episode how to maximize the use of visuals in your classroom. Don't forget to subscribe. Hello and welcome to tier one interventions podcast where we share tips, techniques and strategies to strengthen your core, the core classroom that is, without a core classroom, we cannot thrive. Learn how to create inclusive climate, culture and environment in the regular tier one poor classroom by collaborating with the regular classroom teacher, intervention specialist, instructional coaches, occupational and speech therapists and other direct service providers. Collaboration is key maximizing the learning of all students, particularly those with learning disabilities. By working together we can significantly reduce the need for tier two and tier three, and many pullout interventions. Today we're going to delve into what is that visuals generally? Let's get started and figure out how do visuals impact and create a strong core. And when we say the word impact, we mean inclusion, metacognition, perseverance, adaptability, curiosity, and transcendence. Taken away my friend phrase

Jonily 1:28
I want to start with today is a picture's worth 1000 words. And I want to keep coming back to that today. This is probably the most powerful session as far as high level math achievement for our most struggling kids, when we have kids with any kind of learning disability, and or ADHD processing issues, autism, kiddos who are neurodivergent students that have dyslexia, dysgraphia, and most specifically, discount Kulia. These kiddos struggle with very common themes, things like pattern recognition, most of all math, symbols, notations, math equations, math, symbolic structure, Algebra notation, many of these things are completely foreign to students. Even if we teach and reteach and intervene on these symbols, notations, step by step procedures, algorithms, all of these things that are typical traditional mathematics that some students actually thrive with. And those are the students that end up in these advanced and honors math courses. If you can see and distinguish between symbol and notation of mathematics, if you can capture the very traditional typical language of mathematics, you are going to thrive. Now I'll say this in a couple ways, you're going to thrive with typical traditional progression in school, as far as mathematics, you end up in those advanced classes, you'll score high on tests. But there are two types of kiddos that achieve high One type is everything that I've just described. They can decipher it themselves, but yet really don't have a true deep mathematical sense. These are kids we sometimes call false positives, because they can mimic and grab onto the language and replicate the procedures that the teacher is teaching and score high and end up in these advanced classes. But anytime they're asked to do some kind of mathematics out of context, or maybe on more of a comprehensive maybe on a CT, a CT is a good example where kids have achieved high mathematically their entire school career, and then all of a sudden their math score on the AC T is lower. So these are one group of those high achieving kids. And one thing we can do about that is follow the strategies I'm going to teach today with this phrase a picture's worth 1000 words, because these kids can use that it's actually going to fill some minor gaps that are going to increase their achievement, even though their achievement is already high. The second group of these high achieving kids are kids who, yes, they're achieving high but yes, they have an innate intuitive sense of the mathematics without even being taught the mathematics. As a matter of fact, sometimes the second group of hierachy Even kids has a better understanding conceptually of the mathematics than the teacher does. What we are trying to do, especially with Tier One interventions, is those two groups. Okay, we're good. We're trying to take all of these other kiddos that struggle, our average kids are typical kids who maybe perform well in class, but they just can't capture the high scores on tests, or kids that are always struggling in class, they're always struggling to pay attention to grasp the mathematics, these kids that have some kind of learning disability, specifically dyscalculia, also dysgraphia, dyslexia, ADHD, today's session is for those kids. What we are going to do today, the end game of today is to create visual images for mathematics, connect them to the notation to allow these kids that have never had access before, to gain access to high level complex mathematics. And in our research, our action research and the work that I've done with this model that we're going to share today, some of these kids actually start to test into advanced math courses. And then we have to caution ourselves, because if they end up in an advanced math class that is taught very traditionally, typically, they're not going to have that access, they need these instructional delivery techniques to gain the access to that typical traditional mathematics. That's a broad overview. Some of it probably makes sense. Some of it may not make sense. But a picture is worth 1000 words is how we're going to deliver today's content. What this means for mathematics is, every number has to have a visual image, every number has to have a spot in a pattern, every number has to tell a story. And one of the best stories I like numbers to tell is what shape does the number make. And if students can start to see every number symbol, as a shape, or as chunks of shape, they're going to improve their sense of number. Number Sense is the innate intuitive understanding of the magnitude of a number. Magnitude meaning the size of a number, how large or small a number is, and where that number is placed on a number line. Number Sense is something that we're born with. All animals can count. And what that means is if you think of predator prey situations, I know as the prey, I'm going to stick in packs, because there's more number, I'm less likely. Now, animals aren't rationalizing this, but they have this intuitive innate sense of if I stick with a pack, I'm less likely to be the one that's devoured, for lack of a better word. So predator knows. When I'm looking at the pack, how can I see how many there are and make decisions on whether I'm going to attack. So all animals have this innate intuitive sense of number. However, all animals have a variation of this sense. Some have a stronger, high level sense, some have a weaker sense. And think of the predator prey situation. If you don't have a strong sense of number. You're going to be caught in those dangerous situations in the wild. Now thinking about humans, were born with the same level of understanding of number some of us are born with a higher understanding. Some of us are born with a little weaker number sense. Johns Hopkins University released a study in 2011. So just for a reference for one reference on one of the resources I use to explain this research and even research that I've done is the research that Johns Hopkins University has done, released in 2011. That explained how they proved that babies as young as six months old Have this intuitive innate sense of numbers, some strong and some weak. And then as they follow these babies through toddler years, and then school math years, they replicated this understanding that I'm sharing with you today is this foundation of why visuals are so important. Visuals are going to help us assess the amount of sense of number that kids have tools are going to help us assess the amount of sense of number that kids have, and visuals are going to help us teach and fill gaps for kids that don't have a strong number sense.

The bad part is number sense cannot be taught. So we cannot explicitly directly teach number sense to students. However, number sense can be learned. And number sense can be improved, through experiences that we as the teachers, intervention specialists, facilitators, therapists, the experiences that we provide. And the number one experience for improving number sense, is seeing numbers as visual. Hence, a picture's worth 1000 words. The number one way to use visuals to increase math achievement, is using things as simple as dots. So I want you to keep this in mind and have a collection of these when you're doing math instruction with kids. And that is dominoes and dice, dominoes and dice have certain arrangements of dots. That will help us assess how strong or weak a student's sense of number is, by showing them quickly any dots on dice and dominoes. And asking them without counting individually, how many dots Did you see, I can assess these. I'm gonna I'm gonna use two words here, these estimation skills. But more formally, these subitizing or subitizing skills subitizing, or subitizing, is being able to look at a die rolled. And there are five dots and the number five and on every set of dice. The number five has the same visual arrangement of dots, we can start to see dots as this visual image, then we can connect that visual image to the symbol and the number and the digit five. As we're having students start to write numbers. Dominoes and dice are going to have these arrangements of dots that we want students to begin to Suba ties. And what that means is we want them to look at the dots and be able to tell how many dots without counting. Now the reason I like Domino's is you get more than six dots on many domino games. On some domino games, you'll end up with two lines of four dots. But then, lines have three dots in the center. So you're going to end up with more than eight dots on a domino. It is said that we can only look at chunks of seven and Suba ties or subitize, meaning any more than seven dots, I can't automatically look at it and say how many there are unless and this is one of our techniques for tier one interventions. And less those dots are arranged in rectangular chunks on Domino's, and the way that the dots are placed on Domino's, when stead of now looking at five dots, and just saying there's five, I can actually look at an arrangement of five dot patterns, where each of the individual dots are chunks of dots. For example, instead of one.in, the upper right corner of five, there might be a chunk of 16 Dots, a four by four square. As I look at those chunks, and I can see that square that rectangle, that special rectangle that's a square that's a four by four. I can actually chunk that four by four know that it's 16. And so 16 is one of those chunks. And if I have five of those chunks of 16 I know I have five six teams, and I can start to visualize what five six teams look like. and I can start to compute how much five sixteens are with the arrangement of the dots. And I can separate the dots so that I can get chunks of 10s and sixes. And then two of my sixes can combine for a 10 and a two. So these chunks of dots are what we want to use for regular math instruction to help students understand and count numbers. Dots are a focus trigger. And let me explain what a focus trigger is. So many of us, adults, kids have so many distractions every minute of the day. How do we focus enough so that we learn new information, we can focus through what Sherry and I call focus triggers, focus triggers can be like I'm talking about today, a picture can be a video, it can be an emotional experience that I remember, a focus trigger could be a smell, it could be a sound, it could be a hot or cold feeling. A focus trigger, though, for today's purposes, can be a set of dots that represent a number or pattern of numbers. By using dots as focused triggers, students can understand number better. This is what I mean by number sense can be improved, but not explicitly taught. I can improve number sense by giving students focus triggers in the shape of dots and using dots to help students understand mathematics. The visual is what we call conceptual understanding of mathematics. And this is much easier to do at the elementary level. At the elementary level, when we're looking at Whole numbers and numbers within 100. We can have blocks, we can use manipulatives, we can use tiles, we can use circle counters, and we can very easily represent number with these pictures. at the secondary level that gets more difficult when I have notation, such as equations with variables on both sides. Equations with exponents, variables with exponents, things like two to the negative three, or the square root of 16. These notations and symbols become much more difficult for us as the teachers and facilitators to structure a visual to help connect and give access to the symbols and notations in mathematics. In tier one interventions, that's exactly what we do all the way through the secondary level. There are not many models today that help students gain access to math symbols and notations at the secondary level. And dots will also do that. When we are looking at visual, we're actually using what some call a CRA approach. Concrete representational abstract. If I want dots to be concrete, I can use paper plates with dot stickers. I can use magnetic cookie sheets with magnetic dot circles. And I can actually have kids create and replicate the dot patterns that I want them to understand. I can also use things like egg cartons, where kids can physically touch the bottom of an egg carton really becomes my dot pattern. Or I can open up an egg carton and I can fill it with manipulative.

So this CRA approach to math instruction, concrete representational abstract, with some of the examples that I've just shown, gives you the concrete instructional experience that many kids are going to need. And at the secondary level, kids still need those experiences. representational then, is when I might use graph paper or grid paper to have kids replicate those dark patterns. It's a semi concrete approach. It's still visual, but they're not actually touching the number of dots or the number of things. This progression ends with abstract where we look at these visuals we have kids create these visuals. We have kids make sense of these visuals then And we, as the instructional facilitator, connect these visuals and these pattern dot arrangements, to the math, symbols and notations. Now, this is not how we were taught in school. And so we need to be taught as the adults, especially at the secondary level, how do we use these visuals, and this CRA concrete representational abstract approach to help students gain much more access to secondary high level math, mathematics. And what's going to happen is our most struggling students, our students with a lot of math needs our students with dyscalculia, our students with learning disabilities are going to achieve higher in mathematics. And they're going to start to end up and testing into some of our advanced math courses. And we've seen this throughout our work. Sherry, I don't even know what question I have for you. But what are your thoughts on all of that? What are the struggles that kids have? What are the deficits that kids have with visual perceptual? What are many of the positive aspects of classroom teachers using visuals to gain access to the curriculum and specifically the math curriculum? What is happening in the brain that is going to support what we're trying to teach in tier one interventions. I'm going to let you take it away a little bit and make some of these connections for us through cognitive science and neuroscience. And you also there's another thing you said, I'm giving you a lot right now, I know that you always talk about what the brains crave and what toddlers naturally do. Like, I'm asking you like 52 questions at once, but you just take it away and give us your insight on how cognitive science matches what we're talking about content wise. And

Cheri Dotterer 21:56
that's where we're going to end today. Tune in in two weeks to hear the rest of this conversation.

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